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| Percival D.B., Walden A.T. — Wavelet methods for time series analysis |
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| Предметный указатель |
Fractionally differenced (FD) process, log multitaper WLSE 379
Fractionally differenced (FD) process, log periodogram LSE 379
Fractionally differenced (FD) process, long memory property 284
Fractionally differenced (FD) process, LSE 374 390
Fractionally differenced (FD) process, MLE 361—362
Fractionally differenced (FD) process, MLE, versus WLSE 378
Fractionally differenced (FD) process, octave band average 343 353
Fractionally differenced (FD) process, OLSE 378
Fractionally differenced (FD) process, OLSE, versus WLSE 378
Fractionally differenced (FD) process, parameter and properties 285—286
Fractionally differenced (FD) process, parameter estimation via DWT coefficients 341
Fractionally differenced (FD) process, partial DWT 342
Fractionally differenced (FD) process, reduced log likelihood 363 389
Fractionally differenced (FD) process, sample ACS 341 350
Fractionally differenced (FD) process, SDF 282 284 343—344 348—349
Fractionally differenced (FD) process, simulation 283 341
Fractionally differenced (FD) process, simulation, covariance matrix 356
Fractionally differenced (FD) process, simulation, example 358
Fractionally differenced (FD) process, simulation, via inverse DWT 341 355 389
Fractionally differenced (FD) process, true versus simulated ACVS 357
Fractionally differenced (FD) process, WLSE 374 376 391
Fractionally differenced (FD) process, WLSE and exact MLEs 377—379
Fraedrich, K. 557
Frazier, M.W. 562
frequency 22
Frequency band ANOVA 208 214 233 250—251
Frequency response function (transfer function) 25 33—34 267
Frequency reversal property 211 348
Frequency, negative 22
Frequency, physical 221
Frequency, positive 22
Frequency-based ANOVA 267
Frequentist view 264
Frick, P. 552
Friehe, C.A. 557
Fukao, S. 561
Full-band series 84—85 211
Fuller, W.A. 16 255 299 343 441 555
Function estimation 393
Function of RVs, mean of 256 258
Function, autocorrelation 38
Function, dilation of 457—458 474 494
Function, finite energy 457 459
Function, finite energy, detail of 479—480 497
Function, finite energy, MRA of 478—479 481—482 496
Function, finite energy, wavelet coefficients for 479—480 497
Function, Fourier transform of 37
Function, inverse dilation of 459
Function, regularity of 457 486
Function, scaling see "Scaling function"
Function, square integrability condition (real-valued) 458 494
Function, support of 465
Function, translation of 457—458 474 494
Functions, convolution 38
Functions, cross-correlation 38
Functions, inner product of real-valued 460
Gain function 25
Gamage, N.K.K. 295 555
Gamma function 257
Gao, H.-Y. 79 106—107 135 141 149—150 159 241 253 272 400 432 435 437 439 456 553—555
Gao, W. 6 295 555
Garrote (nonnegative) 456
Gaussian (normal) mixture model 361 410 413 415 417 451
Gaussian (normal) PDF 3 256—357 456
Gaussian (normal) PDF, first derivative 3
Gaussian (normal) PDF, percentage points for standard 257
Gaussian (normal) PDF, second derivative 3
Gaussian (normal) RVs, cumulative distribution function for 257
Gaussian (normal) RVs, IID 291—292
Gaussian (normal) RVs, independent 259
Gaussian (normal) RVs, mean for 257
Gaussian (normal) RVs, PDF for jointly 259
Gaussian (normal) RVs, standard 257
Gaussian (normal) RVs, sum of two independent 451
Gaussian (normal) RVs, uncorrelated 259
Gaussian (normal) RVs, variance for 257
Gaussian (normal) stationary processes, simulation with known ACVS 290—291
Gaussian (normal) stationary processes, simulation with known SDF 291 436
Gaussian noise 440
Gaussian spectral synthesis method (GSSM) 291 357
Gelman, A. 266 555
Generalized Cauchy (t) PDF 258
Generalized Cauchy (t) PDF, mean for 258
Generalized Cauchy (t) PDF, variance for 258
Generalized gaussian distribution 257 417
Geophysical signal analysis 4
Geweke, J. 379 555
Global thresholding 399
Gneiting, Ò. 290 556
Godfrey.R. 411—412 415 556
Gollmer, S.M. 6 556
Gonialves, P. 552
Gonzalez-Esparza, J.A. 219—220 556
Gosling, J.T. 564
Goupillaud, P. 4 556
Granger, C.W.J. 277 281 285 556
Graybill, F.A. 532 556 559
Green, P.J. 402 556
Greenhall, C.A. 141 159 205 310 314 321 378 556
Grey-scaled CWT 8 11
Grossmann, A. 11 556
GSSM see "Gaussian spectral synthesis method"
Gu, Y. 558
Guo, H. 558
Guttorp, P. 159 297 310 321 554 560 563
Haar approximation space, scale one half 461
Haar approximation space, scale two 461
Haar approximation space, scale unity 460—461
Haar CWT 10 13
Haar detail space, scale one half 475
Haar detail space, scale one quarter 475
Haar detail space, scale unity 475
Haar DWT 62 63 156 441
Haar DWT, matrix 57—58 157
Haar DWT, partial 13—14 55
Haar MODWT 17—18
Haar scaling filter and support of Haar scaling function 465
Haar scaling filter of second level 40
Haar scaling filter, autocorrelation width of jth level 103
Haar scaling filter, coefficients 75 463 489
Haar scaling filter, squared gain function 73 76
Haar scaling filter, squared gain function, of second level 91
Haar scaling function 460—463 479
Haar scaling function, direct sum illustrated 472—473
Haar scaling function, support via Haar scaling filter 465
Haar wavelet filter 60 155—156 192
Haar wavelet filter of second level 40
Haar wavelet filter, coefficients 75 480
Haar wavelet filter, phase function 158
Haar wavelet filter, phase function, of jth level 158
Haar wavelet filter, squared gain function 73
Haar wavelet filter, squared gain function, of second level 91
Haar wavelet function 475 479
Haar wavelet function, alternative formulation 2 3 9
Haar wavelet function, alternative formulation, autocorrelation width 12
Haar wavelet function, alternative formulation, repealed 10
Haar wavelet function, alternative formulation, shifted 9 10
Haar wavelet function, half-band filter 76 152
Haar wavelet function, half-band series 84—85 211
Haar wavelet function, hard thresholding 399 412 430 444 453
Haar wavelet function, hard thresholding and consistency 456
Haar wavelet function, hard thresholding, D(4) and LA(8) partial DWTs 418 420
Haar wavelet function, hard thresholding, LA(8) MODWT 430
Haar wavelet function, hard thresholding, LA(8) partial DWT 419—420
Haar, A. 57 556
Habbal, S.R. 564
Haerdle, W. 107 556
Hamming, R.W. 20 179 556
Hannan, E.J. 255 556
Harshvardhan 556
| Harte, D.S. 290 555
Hatanaka, M. 277 556
Healey, D.J. 553
Henson, V.E. 20 553
Herley, C. 457 562
Hermitian transpose 45 47 53 441
Hertz (Hz) 48
Hess-Nielsen, N. 118 231 556
Hidden Markov model (chain or tree) 450—451 455
Hidden state variable 450
High-pass example 26 39
High-pass filter 27
High-pass filter, Daubechies wavelet filter 73—74
High-pass filter, example of impulse response 26 39
High-pass filter, example of use 27
High-pass filter, transfer function 27 39
Higuchi, H. 340 559
Hill, F. 558
Hinkley, D.V. 434 555
Hipel, K.W. 361 559
HMM see "Hidden Markov model"
Hoelder exponents 487
Hoelder regularity 487
Hoelder regularity, D(L) scaling and wavelet functions 487
Hoelder spaces 487
Holden, A.V. 340 556
Homogeneous wavelet expansion 482
Horbury, T.S. 219 552
Hosking simulation method 291
Hosking, J.R.M. 281 285 291 367 556
Howe, D.A. 556
Hsu, D.A. 380 556
Hudgins, L.H. 295 303 557
Hurst coefficient (parameter) 279 286 299
Hurst, H.E. 191 557
Hurvich, C.M. 379 424 557
Hwang, W.-L. 554
Hyperparameter 264—265 413—414 426—427
Hz (Hertz) 48
Ideal risk 420
Identity matrix 42
IID see "Independent and identically distributed"
Imaginary component of complex variable 20—21
Imaginary number 20
Impulse response sequence 25
Inclan, C. 380—381 557
Inconsistency of periodogram 270 298
Independence and uncorrelated Gaussian (normal) RVs 259 407
Independent and identically distributed (IID) RVs 262 288 393 398 452
Independent and identically distributed (IID) RVs, Gaussian (normal) 291—292 417 453
Independent and identically distributed (IID) RVs, Gaussian (normal), and chi-square RV 293
Independent and identically distributed (IID) RVs, Gaussian (normal), noise DWT coefficients 418
Independent and identically distributed (IID) RVs, Gaussian (normal), wavelet coefficients 417
Independent rvs 258 260
Independent signal and noise 452
Independent signal DWT coefficients 451
Indicator function 404
Infinite sequence, autocorrelation 25 36
Infinite sequence, convolution 24 36
Infinite sequence, cross-correlation 24 36
Infinite sequence, discrete Fourier transform of 21 35 39
Inhomogeneous wavelet expansion 482
Inner product, complex 45
Inner product, preservation via orthonormal transform 54
Inner product, real 4*2
Inner product, real functions 460
Instantaneous frequency 158 322
Instantaneous long memory parameter estimation, LSE 379 391
Instantaneous long memory parameter estimation, LSE, variance 392
Instantaneous long memory parameter estimation, MLE 374 391
Integer part 214
Integers (set of Z) 458
Inter-quartile range 442
Interplanetary shock waves, corotating 219
Interplanetary shock waves, transient 219
Interpolation operator 103
Intersection of events 435
Inverse, DFT, finite sequence 29 36 78 291
Inverse, DFT, infinite sequence 22 35 70 267
Inverse, DWT 422
Inverse, DWT, use in simulation of FD process 341
Inverse, Fourier transform of function 37
Inverse, MODWT 175 429
Inverse, MODWT, transform matrix as Moore — Penrose generalized 167 204
Inverse, ODFT 49
Inverse, partial DWT 419 422 425 433—434 445 454
Isometric transform 43 46—47 53
Jacobian 258 261
Jansen, M. 424 557
Jawerth, B. 461 464 557
Jenkins, G.M. 269 317 553 557
Jensen, M.J. 366 374—375 378—379 385 557
Jiang, J. 6 557
Johnson, D.M. 218 558
Johnson, G.E. 290 557
Johnson, N.L. 258 557
Johnstone, I.M. 400—401 406 418 420 444 450 456 555 557
Joint PDF 258 265 409
Joyeux, R. 281 285 556
Kaplan, L.M. 366—367 557
Kashyap, R.L. 364 557
Kay, S.M. 269 292 361 557
Kelly, B.G. 559
Kendall, D.G. 270 275—376 376 553
Kerkyacharian, G. 556
Kim, M. 354 562
Kleiner, B. 554
Kolaczyk, E.D. 554
Komm, R.W. 450 558
Koopmans, L.H. 119 255 269 558
Kotz, S. 557
Krim, H. 560
Kronecker delta function 43
Kumar, P. 4—6 12 295 555 560
Kuo, C.-C.J. 366—367 557
Kuo, C.T. 273 558
Kurth, W.S. 564
LA(10) scaling filter, reversal from Daubechies 117
LA(12) scaling filter coefficients 109 112
LA(14) scaling filter, reversal from Daubechies 117
LA(16) scaling filter coefficients 109 112
LA(8) partial DWT basis vectors 162
LA(8) scaling filter 4th level, shift factor 179
LA(8) scaling filter 4th level, squared gain function 97 99
LA(8) scaling filter of jth level 97—98
LA(8) scaling filter of jth level, squared gain function 157
LA(8) scaling filter, coefficients 109 112 494
LA(8) wavelet filter of jth level 97—98
LA(8) wavelet filter of jth level, shift factor 179
LA(8) wavelet filter of jth level, squared gain function 97 99 157
LA(8) wavelet packet filter for node (4,n), advance required 253
LA(8) wavelet packet filter for node (4,n), shift factor 221
LA(L) scaling filter 107 112 117 155
LA(L) scaling filter of jth level, advance required 156
LA(L) scaling filter of jth level, shift factor 114 158 198 205
LA(L) scaling filter, advance required 113 156
LA(L) scaling filter, approximately linear phase 112 117
LA(L) scaling filter, phase function 112
LA(L) scaling filter, plotted 98 112—113 119
LA(L) scaling filter, shift factor 229
LA(L) scaling function, Hoelder regularity 494
LA(L) wavelet filter 97—98
LA(L) wavelet filter of jth level, advance required 146 155
LA(L) wavelet filter of jth level, phase after advance 114—115 120
LA(L) wavelet filter of jth level, phase function 112
LA(L) wavelet filter of jth level, plotted 98 112—113
LA(L) wavelet filter of jth level, shift factor 114 198 205
LA(L) wavelet filter of jth level, time shift function 119 121
LA(L) wavelet filter, advance required 113
LA(L) wavelet filter, approximately linear phase 112 188
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